Question

Suppose that the function g is defined, for all real numbers, as follows.

g(x)= { -1/4x +1 If x< -2

-(x+1)^2+1 If -2 ≤ x ≤ 2

2 If x>2

Find g(-2), g(-1), and g(4)

Answer 1

a) g(-2) = 0

b) g(-1) =1

c) g(4) = 2

Explanation:

Given data

`g(x) = (-1)/(4x+1) if x < -2`

`g(x) = - (x+1)^(2) +1 if -2\leq x\leq 2`

`g(x) = 2 if x >2`

Step( i ):-

`g(x) = - (x+1)^(2) +1 if -2\leq x\leq 2`

put x = -2

`g(-2) = -(-2+1)^(2) +1 = -(-1)^(2)+1 = -1+1 =0`

g(-2) = 0

Step(ii):-

`g(x) = - (x+1)^(2) +1 if -2\leq x\leq 2`

Put x = -1

`g(-1) = -(-1+1)^(2) +1 = -(0)^(2)+1 = -0+1 =1`

g(-1) =1

Step(iii):-

`g(x) = 2 if x >2`

g(4) = 2